The present invention relates to a method for determining a polarization dependent characteristic of an optical or opto-electronic device. Using the Mueller matrix data, a matrix M corresponding to a difference between a first and a second transmission spectrum is determined. The first and the second transmission spectrum correspond to a first Stokes vector and a second Stokes vector, respectively, with the second Stokes vector being opposite to the first Stokes vector. Eigenvalues of the matrix M are then determined and the first Stokes vector is determined by selecting the largest eigenvalue of the matrix M and determining a corresponding eigenvector. The second Stokes vector is then determined as a vector opposite to the first Stokes vector. Finally, the data indicative of the polarization dependent characteristic of the device are determined using the first and the second Stokes vector and the Mueller matrix data. This method is highly beneficial by providing highly accurate data related to polarization dependent parameters while simultaneously providing a nearly instantaneous result with minimum computational effort.
Legal claims defining the scope of protection, as filed with the USPTO.
1. A method for determining a polarization dependent characteristic of a device comprising: a) receiving Mueller matrix data, the Mueller matrix data being indicative of wavelength dependent first row Mueller matrix elements of the device, the device being one of an optical and an opto-electrical device; b) using the Mueller matrix data, determining a matrix M corresponding to a difference between a first and a second transmission spectrum, the first and the second transmission spectrum corresponding to a first Stokes vector and a second Stokes vector, respectively, with the second Stokes vector being opposite to the first Stokes vector; c) determining eigenvalues of the matrix M; d) determining the first Stokes vector by selecting the largest eigenvalue of the matrix M and determining a corresponding eigenvector; e) determining the second Stokes vector, the second Stokes vector being a vector opposite to the eigenvector; and, f) determining data indicative of the polarization dependent characteristic of the device using the first and second Stokes vector and the Mueller matrix data.
2. A method for determining a polarization dependent characteristic of a device as defined in claim 1 wherein d) comprises scaling the first Stokes vector to unit length.
3. A method for determining a polarization dependent characteristic of a device as defined in claim 2 wherein the matrix M comprises a 3×3 matrix.
4. A method for determining a polarization dependent characteristic of a device as defined in claim 2 wherein the eigenvalues are determined using a Jacobi method.
5. A method for determining a polarization dependent characteristic of a device as defined in claim 2 wherein the first and the second transmission spectrum comprises a predetermined wavelength range.
6. A method for determining a polarization dependent characteristic of a device as defined in claim 5 wherein the predetermined wavelength range comprises a complete operational wavelength range of the device.
7. A method for determining a polarization dependent characteristic of a device as defined in claim 5 wherein the polarization dependent characteristic comprises one of polarization dependent loss and polarization dependent frequency.
8. A method for determining a polarization dependent characteristic of a device as defined in claim 1 wherein the device comprises a plurality of channels, the method comprising: repeating a) to f) for each of the plurality of channels.
9. A method for determining a polarization dependent characteristic of a device as defined in claim 8 wherein for each of the plurality of channels the first and the second transmission spectrum comprises a complete operational range of the corresponding channel.
10. A method for determining a polarization dependent characteristic of a device as defined in claim 8 comprising: swapping the first and the second incident Stokes vector of one channel if a dot product of corresponding incident Stokes vectors of the channel and an adjacent channel is negative.
11. A method for determining a polarization dependent characteristic of a device as defined in claim 8 wherein the polarization dependent characteristic comprises one of polarization dependent loss and polarization dependent frequency for each of the plurality of channels.
12. A storage medium having stored therein executable commands for execution on a processor, the processor when executing the commands performing: receiving Mueller matrix data, the Mueller matrix data being indicative of wavelength dependent first row Mueller matrix elements of one of an optical and an opto-electrical device; using the Mueller matrix data, determining a matrix M corresponding to a difference between a first and a second transmission spectrum, the first and the second transmission spectrum corresponding to a first Stokes vector and a second Stokes vector, respectively, with the second Stokes vector being opposite to the first Stokes vector; determining eigenvalues of the matrix M; determining the first Stokes vector by selecting the largest eigenvalue of the matrix M and determining a corresponding eigenvector; determining the second Stokes vector, the second Stokes vector being a vector opposite to the eigenvector; and, determining data indicative of the polarization dependent characteristic of the device using the first and second Stokes vector and the Mueller matrix data.
13. A system for determining a polarization dependent characteristic of a device comprising: an input port for receiving Mueller matrix data, the Mueller matrix data being indicative of wavelength dependent first row Mueller matrix elements of the device, the device being one of an optical and an opto-electrical device; a processor in communication with the first port for: a) using the Mueller matrix data, determining a matrix M corresponding to a difference between a first and a second transmission spectrum, the first and the second transmission spectrum corresponding to a first Stokes vector and a second Stokes vector, respectively, with the second Stokes vector being opposite to the first Stokes vector; b) determining eigenvalues of the matrix M; c) determining the first Stokes vector by selecting the largest eigenvalue of the matrix M and determining a corresponding eigenvector; d) determining the second Stokes vector, the second Stokes vector being a vector opposite to the eigenvector; and, e) determining data indicative of the polarization dependent characteristic of the device using the first and second Stokes vector and the Mueller matrix data; and, an output port in communication with the processor for providing the data indicative of the polarization dependent characteristic of the device.
14. A system for determining a polarization dependent characteristic of a device as defined in claim 12 wherein the processor comprises electronic circuitry designed for performing at least a portion of a) to e).
15. A system for determining a polarization dependent characteristic of a device as defined in claim 12 comprising a control port in communication with the processor for receiving control commands for controlling a) to e).
16. A system for determining a polarization dependent characteristic of a device as defined in claim 14 comprising a graphical display in communication with the processor for displaying the data indicative of the polarization dependent characteristic in a graphical fashion.
17. A system for determining a polarization dependent characteristic of a device as defined in claim 15 wherein the graphical display comprises a graphical user interface.
18. A method for determining a polarization dependent characteristic of a device comprising: a) receiving Mueller matrix data, the Mueller matrix data being indicative of wavelength dependent first row Mueller matrix elements of the optical device, the device being one of an optical and an opto-electrical device; b) determining a set of first Stokes vectors and a set of second Stokes vectors, each Stokes vector of the set of second Stokes vectors being opposite to a corresponding Stokes vector of the set of first Stokes vectors, the set of first Stokes vectors substantially covering a surface of a hemisphere of a Poincaré sphere; c) using the Mueller matrix data, determining for the first Stokes vector and the second Stokes vector of each pair of opposite first and second Stokes vectors a corresponding first and second transmission spectrum; d) determining for each pair of opposite first and second Stokes vectors a normalized difference between the corresponding first and second transmission spectrum; e) determining the pair of opposite first and second Stokes vectors having the largest normalized difference; and, f) determining data indicative of the polarization dependent characteristic of the device using the pair of opposite first and second Stokes vectors having the largest normalized difference and the Mueller matrix data.
19. A method for determining a polarization dependent characteristic of a device as defined in claim 17 wherein b) to e) are performed for predetermined wavelengths in a predetermined wavelength range, the predetermined wavelength range being smaller than an operational wavelength range of the device.
20. A method for determining a polarization dependent characteristic of a device as defined in claim 18 wherein f) the determination of the data indicative of the polarization dependent characteristic is performed for predetermined wavelengths in the complete operational wavelength range of the device.
21. A method for determining a polarization dependent characteristic of a device as defined in claim 19 wherein the device comprises a plurality of channels, the method comprising: repeating a) to f) for each of the plurality of channels.
22. A method for determining a polarization dependent characteristic of a device comprising: receiving Mueller matrix data, the Mueller matrix data being indicative of wavelength dependent first row Mueller matrix elements of the optical device, the device being one of an optical and an opto-electrical device; using the Mueller matrix data, determining a set of insertion loss data and a set of center frequency data for each of a plurality of input states of polarization substantially covering a surface of a Poincaré sphere; processing the set of insertion loss data and the set of center frequency data for determining extremes of insertion loss and extremes of center frequency; determining a first and a second incident Stokes vector for each of the extremes of the insertion loss and the extremes of the center frequency; determining an orthogonality parameter for the first and the second incident Stokes vector for each of the extremes of the insertion loss and the extremes of the center frequency, the orthogonality parameter having a predetermined value for indicating othogonality; selecting the extreme and the corresponding first and second incident Stokes vector associated with the orthogonality parameter closest to the predetermined value; and, determining data indicative of the polarization dependent characteristic of the device using the selected first and second incident Stokes vector and the Mueller matrix data.
23. A method for determining a polarization dependent characteristic of a device comprising: receiving matrix data indicative of a wavelength dependent influence of the device on a light wave transmitted therethrough, the device being one of an optical and an opto-electrical device; determining a set of first Stokes vectors and a set of second Stokes vectors, each Stokes vector of the set of second Stokes vectors being opposite to a corresponding Stokes vector of the set of first Stokes vectors; using the matrix data, determining for the first Stokes vector and the second Stokes vector of each pair of opposite first and second Stokes vectors a corresponding first and second transmission spectrum; determining for each pair of opposite first and second Stokes vectors a normalized difference between the corresponding first and second transmission spectrum; determining the pair of opposite first and second Stokes vectors having the largest normalized difference; and, determining data indicative of the polarization dependent characteristic of the device using the pair of opposite first and second Stokes vectors having the largest normalized difference and the matrix data.
24. A method for determining a polarization dependent characteristic of a device as defined in claim 22 wherein the matrix data comprise elements of a row of a Mueller matrix.
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June 30, 2006
December 30, 2008
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